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Public Economics 3
Summary notes: Black et al, Chapter 6
Public choice theory
Learning objective
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Discuss the Rawlsian theory of justice and
comment on its relevance to recent political
developments in South Africa
Explain the median voter theory and indicate its
potential strengths and weaknesses
Discuss the meaning and importance (if any) of
Kenneth Arrow’s impossibility theorem
Consider whether logrolling (vote trading) is an
efficient means of improving on the outcomes of
a majority voting system
Explain the theory of ‘optimal voting rules’ and
consider the question of whether it does indeed
provide an ‘optimal rule’ for majority voting
Discuss the maximising behaviour of politicians
and bureaucrats, and consider the implications of
such behaviour for majority voting
Explain what is meant by ‘rent seeking’
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6.1 Introduction
The goal is an understanding of what is sometimes referred
to as the political market place.
The concern is with the way in which this ‘market’
functions to distribute scarce resources (between private
and public sectors, and within the public sector).
Look at the mechanisms by which individual preferences
are translated into social or public preferences.
At the extreme is dictatorial rule – impose the preferences
of one individual.
Some form of collective decision-making/ mass
participation is preferred, ranging from unanimity to
majority rule. Most common social choice rule today in
Western democracies is majority rule.
6.2 The unanimity rule and the Rawlsian
experiment
Unanimity means all members of a community must agree
before a decision is made. It is the only voting rule that
generates a Pareto outcome.
Pareto-reallocations are all positive sum games (nobody is
made worse-off). Bergson redistributions may be zero-sum
(somebody is worse-off because others have been made
better-off).
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John Rawls’ (1971) Theory of Justice is a normative theory
which sets out conditions under which ‘free and rational’
persons choose certain principles of justice that govern the
‘basic structure of society’
The emerging ‘social contract’ is called by Rawls a case of
‘justice in fairness’.
In essence, he asks that we step through a ‘veil of
ignorance’ and imagine a hypothetical ‘original position’ in
which no individual knows in advance what their position
in society will be.
Assuming each participant is equally risk-averse, then
everyone would support a risk-minimising social welfare
function that protects them against the worst outcome:
W = Minimum (Ua, Ub)
This suggests that welfare depends on the lower of the two
individual utilities, i.e., if Ua > Ub, then W = Ua.
Ub can increase over time as long as Ua does not decrease –
thus allowing for Pareto optimality.
With the assumptions used here, all parties would adopt a
maximin strategy. This gives priority to the worst off party
(no redistribution should be attempted if it does not benefit
the worst-off group in society).
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Rational actors (all equally risk averse) will unanimously
choose this in case they land up among the worst-off.
Problems with unanimity rule:
costly
time-consuming
could encourage ‘logrolling’ (vote trading)
the last unpersuaded voter has the decisive vote,
gives minorities veto rights
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6.3 Majority voting and the median voter
Majority rule: ‘50% + one vote’ support before decision is
made.
Direct democracy makes use of referendums to ascertain
the wishes of the people on any issue.
Very costly. Used mainly for important national decisions
(e.g. in SA for change, in Switzerland (1970s) decision to
give women the vote!)
Most common are representative democracies–
individuals elect representatives to make decisions on their
behalf.
This gives rise to the possibility of a political market. This
is a variant of the principal/agent problem that arises (for
example) between managers and shareholders in a firm.
Downs (1957) – politicians wish to maximise votes and
voters wish to maximise the benefits that political power
can dispense. In an ideal world, an important mechanism
for translating individual preferences into social
preferences.
To get at this, we consider the median voter theorem – this
has become increasingly important in today’s politics in
countries like the UK and USA.
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Example: 5 voters, national health budget
Voter
A
B
C
D
E
Preferred
Expenditure (R millions)
50
200
400
600
800
3 out of 5 options will get majority support. All 5 voters
will not object to 50, 4 voters will not object to 200, 3 will
not object to 400.
Which is the optimal one? The best option is that of the
median voter C whose preferences divide the voters in two.
The theorem holds that under majority voting rules, as long
as preferences are not extreme, the median voter’s
preferred option will win. It is the option that minimises
welfare loss. So:
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politicians interact with voters to determine
relative preferences, and
in doing so, they identify the median voter, and
they act on his or her preferences, and
in so doing, fulfill majority wishes at minimum
costs
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Problems of implementation:
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Not all politicians are vote maximisers – many
pursue ‘public’ or ‘national’ interest instead (cf.
the death penalty)
Others may use charisma rather than tangible
benefits to voters
Presumes the median voter can be identified.
Different political issues may have different
median voters (cf. the rise of single-issue social
movements like the greens)
Not everyone will vote and voters may not be
‘rational’.
Politicians and voters are far from perfectly
informed - this makes ‘rational’ choice unlikely
Even though simple majority rule is unlikely to yield
Pareto-efficient outcomes, it has two important advantages
over unanimity rule:
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Obtaining approval for a majority preference
takes less time and is less costly, and
Minorities cannot block majority wishes
The downside of this, of course, is that winner-take-all
systems can (and do) ignore minority interests (the tyranny
of the majority).
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6.4 The impossibility theorem
Majority voting can lead to inconsistent results.
According to Kenneth Arrow’s (1951) impossibility
theorem, there is no single voting system that would meet
all of the ‘ethical’ conditions for an ‘acceptable’ social
choice rule.
The ethical conditions are summarised by Black et al as
follows:
 Rationality assumption. Individuals must either
prefer X to Y or be indifferent between them:
X > Y or Y > X, or X = Y
where > symbolises ‘prefer’ and = stands for
indifferent.
The transitivity condition must also hold:
if X > Y, and Y > Z, then X > Z.
 Independence of irrelevant alternatives. If choice is
between X and Y, then Z has no effect on outcomes.
 Pareto principle.
If (X > Y)a and (X = Y)b then X > Y
 Unrestricted domain. It must be possible for all
eligible voters to vote.
 Non-dictatorship.
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Although these requirements appear reasonable, the Arrow
problem becomes relevant where preferences are widely
divergent or where voters choose extreme alternatives.
Example of voting for 3 sizes of budget.
Choice
First
Second
Third
A
L
M
S
Voter
B
M
S
L
C
S
L
M
Pairing L against M, L wins, 2 to 1
Pairing M against S, M wins, 2 to 1
Pairing S against L, S wins, 2 to 1
If L is preferred to M and M is preferred to S, then
according to the rule of transitivity, L should be preferred
to S.
Running pair-wise competitions where one voter has
extreme preferences (voter C) leads to inconsistency.
Pair-wise competitions are not unheard of in democracies.
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Consequences:
 A different winner every time sequence of voting is
changed. Impossible to get a consistent winner.
Majority voting rule where there are extreme voters
does not produce outcomes supported by the majority
- voting paradox
 The inconsistencies that emerge can lead to vote
cycling (endless pair-wise competitions).
 If election organizers have some prior knowledge can
organise voting sequences to take advantage of this agenda manipulation.
Practical importance? The probability of an outcome that
does not enjoy majority support rises as the number of
voters and numbers of alternatives increase.
With six alternatives and a very large number of voters this
can reach 31%.
This problem is compounded by the fact that differences in
the intensity of preferences are not taken into account in
majority voting.
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6.5 Majority voting and preference intensities
Majority voting rule doesn’t take into account intensity of
voters’ preferences, very costly to do so.
If the majority has a weak preference for a candidate or
issue and a minority has strong objections, then depending
on relative numbers, majority rule could reduce society’s
welfare.
There are two ways to address this:
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Weighted votes – rather than yes-no, voter is
allowed, say, 100 points and can express intensity
by allocating between choices.
Problems: Weighting is a normative procedure.
Administratively costly and difficult to
implement.
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Vote trading (logrolling) – minority and majority
groups exchange support among issues, or
minorities ‘gang up’ against a majority.
Problems: ‘You scratch my back and I’ll scratch
yours’ approach can easily lead to adoption of
non-viable projects.
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Examples: Logrolling allows voters to express the intensity
of their preferences by trading votes.
Voter
Project
Hospital
Library
Pool
A
200
-40
-120
B
-50
150
-60
C
-55
-30
400
Total net
benefits
95
80
220
Three voters, figures indicate benefits (losses) for each
project.
On straight vote, all projects rejected, despite net positive
benefits for each.
If voting on each project takes place one at a time, A agrees
to vote for library if B votes for hospital. Both are
accepted.
Then A agrees to vote for pool if C votes for hospital, etc
However, agenda control still affects the provision of
public goods, and minority gains may come at the expense
of greater general losses.
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Voter
Project
Hospital
Library
Pool
A
200
-40
-120
B
-110
150
-140
C
-105
-120
400
Total net
benefits
-15
-10
-10
Suppose A offers to support library in exchange for B’s
vote for hospital ---- both score and deal goes through
despite negative benefits.
B and C trade votes for pool and library, etc
Logrolling can sometimes improve welfare, but this is not
always the case.
6.6 Optimal voting rules
Something between 100% unanimity and simple majority
(50% plus one vote) is offered by Buchanan and Tullock’s
(1962) ‘optimal voting rules’,
Optimal voting rules vary with the issue at hand and
depend on the cost involved.
This approach compares two sets of costs involved in
voting:
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External costs. Essentially, this measures the
degree of unhappiness amongst those who lose in
a referendum or vote. These costs will be highest
in a dictatorship, and zero if complete unanimity
is achieved.
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Decision-making costs. The larger the voting
community, the more costly it is to reach a
majority decision. Opportunities to free ride also
increase as the size of the group increases.
See Figure 6.1 on p.76.
The optimal majority for any issue occurs where the sum of
decision-making and external costs is a minimum (M*).
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An important variable to consider here is homogeneity –
communities in which there are sharp differences between
sub-groups (the norm in most societies?) will incur high
costs in trying to secure near-unanimity decisions.
Vociferous minorities will raise external costs – they will
thus press for high majorities. Low external costs, by
contrast, would require lower majorities.
An example: two-thirds majority needed in SA for
constitutional change.
6.7 Government failure: Politicians and
bureaucrats
Government failure can nullify the results of any properlyconducted referendum or election. It can come about in
three ways:
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Rational behaviour by politicians pursuing votemaximising strategies
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Rational behaviour by bureaucrats (maximising
utility by pursuing incentives created by
bureaucratic structures)
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Rational behaviour by citizens and interest groups
engaged in rent-seeking
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The economic theory of politics proposed by Downs in
about 1957 views politicians as entrepreneurs using votemaximising strategies to secure and retain office.
Two other characteristics of majority voting rules:
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Rational ignorance of voters – acquiring
information on what politicians actually stand for
is so costly that it is rational to remain ignorant.
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Politicians are elected on the basis of a package
of policies and hence do not need to satisfy a
majority on every issue.
Taken together, these properties of the system can lead to
implicit logrolling outcomes.
The text uses a rugby development programme,
parliamentary relocation to Pretoria and a subsidised loan
scheme for students as the three issues.
Three special interest groups strongly in favour of one of
three and weakly opposed to the other two (on which they
may remain rationally ignorant). Would rather have all
three than none. The politician supports all three - has an
incentive to make benefits known to particular interest
group and to understate the costs of the programmes to
electorate as a whole.
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Two outcomes may be expected:
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Lots of special interest legislation producing a
variety of relatively unpopular public goods, and
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An aggregate over-supply of public goods in
society
Buchanan and Tullock (1962) argue that this is evidence of
constitutional failure. Propose a constitutional limitation
on the size of government (fixed percentage of national
income, and specified distribution between different kinds
of public goods).
No government has yet gone that far – however, the
influence of the ‘Washington consensus’ has achieved
some of their goals.
Another source of government failure is bureaucratic
failure – bureaucrats maximize utility in the face of
incentives offered to them by bureaucratic structures.
Niskanen (1971) argued that since salaries, power, prestige
and other favourable attributes are positively related to
bureau size, and hence bureau budget, bureaucrats have a
tendency to maximise budgets.
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Bureaucratic failure is an example of a principal-agent
problem.
Bureaucrats act as agents for taxpayers (the principals),
represented by elected politicians.
Bureaucrats have the strong incentive identified above to
maximise budgets/expenditure.
Individual taxpayers benefit only marginally from that
expenditure– they remain rationally ignorant.
Organisational difficulties prevent taxpayers from lobbying
against higher taxes and in favour of lower expenditure.
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6.8 Rent-seeking
Another possible source of govt. failure/economic
inefficiency as a result of govt. intervention that creates
distortions leading to income and wealth transfers to private
individuals/ interest groups.
Economic rent – that part of the reward accruing to
resource owners over and above the payment that the
resources would have received in any alternative
employment.
In a perfectly competitive market, rent is competed away
(like profits).
But if govt. protects monopoly power for instance, this
artificially creates rent. Individuals or interest groups will
compete for this rent, and the resources spent on trying to
obtain the rent could have been used productively
elsewhere (a source of allocative inefficiency).
See Figure 6.3, p. 81. Shows a competitive market. What
happens if govt. intervenes to restrict output? Price rises,
wealth is transferred from consumers to producers (AE0E1 =
deadweight loss).
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But there is an additional welfare loss to society –
potential producers will try to ‘capture’ that surplus to
boost profits by lobbying govt. and in the process incurring
additional costs (MC would increase – but additional
profits would still be made). Or if consumers try to lobby
govt. to reduce output, they will incur costs external to the
producers. In either case, these resources are wasted/used
non-productively.